The primary objectives are: a) to assess the magnitude of extracellular neutrophil elastase (HNE) inhibitory activity in BAL fluid following 14 days of oral DMP777 administration twice daily (bid) (every 12 hours) or three times daily (tid) (every 8 hours) in adult patients with cystic fibrosis (CF); b) to correlate this effect with any observed changes in extracellular HNE activity in BAL fluid with systemic pharmacokinetic (PK) and pharmacodynamic (PD) data; and c) evaluate the safety of DMP777. The secondary objective is to determine the correlation between the magnitude of BAL extracellular HNE inhibition and improvement in biological indices relevant to the pathogenesis of lung disease in CF.